Also, when you choose to save a connection, select the restorable connection option on the save dialog. The same dialog also gives you the option of saving your password, although for security reasons this is unchecked by default. If you don't save the password, you'll be prompted to enter it at startup. (You only have the enter the password once if multiple connections use the same credentials.)
I designed it that way because I've worked in a number of environments which are highly security-conscious, and as a result I've largely internalized the "secure by default" way of thinking. As noted, you can save the password along with the connection, but I only recommend doing that if you have full, private control over the computer.
BTW, since the client is based on NetDrive, you can also use the ndctl option to save and restore connections automatically - this basically has the same effect as saving all connections along with their passwords. (This involves hand-editing ndctl.cfg and setting the PersistentVolumeConfiguration option. Again, this is not considered secure if other people may have access to the computer.) Don't do this if you use the ArcaMapper 'restore connections on startup' option, because if you do it'll end up trying to restore connections twice.